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Chapter 4: Problem 38

Rewrite each fraction with the indicated denominators. $$\frac{7}{4}=\frac{ }{32}$$

Short Answer

Expert verified
\( \frac{7}{4} = \frac{56}{32} \).

Step by step solution

01

- Identify the new denominator

The given fraction is \( \frac{7}{4} \) and the new denominator should be 32.
02

- Determine the multiplication factor

To rewrite the fraction with the new denominator, find the factor that 4 must be multiplied by to get 32. This is done by dividing the new denominator by the original denominator: \[ \frac{32}{4} = 8 \]
03

- Multiply both numerator and denominator

Multiply both the numerator and the denominator of the original fraction by this factor: \[ \frac{7 \times 8}{4 \times 8} = \frac{56}{32} \]
04

- Write the final answer

Now, the fraction with the new denominator is \( \frac{56}{32} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rewrite Fractions
Rewriting fractions is a method to change the form of a fraction without changing its value. This is useful for comparing fractions, adding or subtracting them, or converting to a common denominator.

For example, consider the fraction \( \frac{7}{4} \). To rewrite this fraction with a new denominator, you follow a few straightforward steps.

  • First, identify the new denominator.
  • Second, determine the factor you need to multiply the original denominator by to get the new denominator.
By following these steps, you can successfully rewrite a fraction while maintaining its value.
Multiplication Factor
The multiplication factor is crucial when rewriting fractions. It helps you convert the fraction to have a new denominator. To find this factor, divide the new denominator by the original denominator.

In our example, for \( \frac{7}{4} \) to be rewritten with a denominator of 32, you'd calculate:
\[ \frac{32}{4} = 8 \]

This result means you need to multiply both the numerator and the denominator of \( \frac{7}{4} \) by 8. Doing this keeps the value of the fraction the same.
Denominators
Denominators are the bottom numbers in a fraction. They indicate how many equal parts the whole is divided into.

When working with fractions, matching denominators can be crucial when performing operations like addition or subtraction.
In the exercise, the denominator is changed from 4 to 32. By rewriting the fraction with a common or specified denominator, you ensure consistency in comparisons and arithmetic operations.

To change the denominator without altering the fraction鈥檚 value, you use the concept of the multiplication factor, multiplying both the numerator and the denominator by the same number.

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